Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Breaking of Henry's law for noble gas and CO2 solubility in silicate melt under pressure


Degassing of the Earth is still poorly understood, as is the large scatter in He/Ar ratios observed in mid-ocean ridge basalts. A possible explanation for such observations is that vesiculation occurs at great depths with noble-gas solubilities different from those measured at 1 bar (ref. 1). Here we develop a hard-sphere model for noble-gas solubility and find that, owing to melt compaction, solubility may decrease by several orders of magnitude when pressure increases, an effect subtly overbalanced by the compression of the fluid phase. Our results satisfactorily explain recent experimental data on argon solubility in silicate melts, where argon concentration increases almost linearly with pressure, then levels off at pressures of 50–100 kbar (refs 2–5). We also model vesiculation during magma ascent at ridges and find that noble-gas partitioning between melt and CO2 vesicles at depth differs significantly from that at low pressure. Starting at 10 kbar (35 km depth), several stages of vesiculation occur followed by vesicle loss, which explains the broad variability of He–Ar concentration data in mid-ocean ridge basalts. ‘Popping rocks’, exceptional samples with high vesicularity, may represent fully vesiculated ridge magma, whereas common samples would simply have lost such vesicles.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Calculated solubility parameters of pure noble gases in a tholeiitic melt at 1,673 K as a function of pressure.
Figure 2: Calculated argon concentration (weight fraction) for pure argon in contact with haplogranite, tholeiite and olivine melts, as a function of pressure.
Figure 3: Evolution of the vesicularity of a MORB with pressure during magma ascent.
Figure 4: Calculated 4 He/ 40 Ar ratio compared with measurements for MORBs.


  1. Sarda, P. & Moreira, M. Vesiculation and vesicle loss in mid-ocean ridge basalt glasses: He, Ne, Ar elemental fractionation and pressure influence. Geochim. Cosmochim. Acta 66, 1449–1458 (2002)

    ADS  CAS  Article  Google Scholar 

  2. White, B. S., Brearley, M. & Montana, A. Solubility of argon in silicate liquid at high pressures. Am. Mineral. 74, 513–529 (1989)

    ADS  CAS  Google Scholar 

  3. Carroll, M. R. & Stolper, E. M. Noble gas solubilities in silicate melt and glasses: new experimental results for argon and the relationship between solubility and ionic porosity. Geochim. Cosmochim. Acta 57, 5039–5051 (1993)

    ADS  CAS  Article  Google Scholar 

  4. Chamorro-Perez, E., Gillet, Ph. & Jambon, A. Argon solubility in silicate melts at very high pressures. Experimental set-up and preliminary results for silica and anorthite melts. Earth Planet. Sci. Lett. 145, 97–107 (1996)

    ADS  CAS  Article  Google Scholar 

  5. Schmidt, B. C. & Keppler, H. Experimental evidence for high noble gas solubilities in silicate melts under mantle pressures. Earth Planet. Sci. Lett. 195, 277–290 (2002)

    ADS  CAS  Article  Google Scholar 

  6. Andersen, H. C., Weeks, J. D. & Chandler, D. Relationship between the hard-sphere fluid and fluids with realistic repulsive forces. Phys. Rev. A. 4, 1597–1605 (1971)

    ADS  Article  Google Scholar 

  7. Carnahan, N. F. & Starling, K. E. Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51, 635–636 (1969)

    ADS  CAS  Article  Google Scholar 

  8. Song, Y. & Mason, E. A. Statistical-mechanical theory of a new analytical equation of state. J. Chem. Phys. 91, 7840–7853 (1989)

    ADS  CAS  Article  Google Scholar 

  9. Bottinga, Y., Richet, P. & Weill, D. F. Calculation of the density and thermal expansion coefficient of silicate liquids. Bull. Minéral. 106, 129–138 (1983)

    CAS  Article  Google Scholar 

  10. Reiss, H., Frisch, H. L., Helfand, E. & Lebowitz, J. L. Aspects of the statistical thermodynamics of real fluids. J. Chem. Phys. 32, 119–124 (1960)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  11. Guillot, B. & Guissani, Y. The solubility of rare gases in fused silica: a numerical evaluation. J. Chem. Phys. 105, 255–270 (1996)

    ADS  CAS  Article  Google Scholar 

  12. Jambon, A., Weber, H. & Braun, O. Solubility of He, Ne, Ar, Kr, Xe in a basalt melt in the range 1250–1600 °C. Geochemical implications. Geochim. Cosmochim. Acta 50, 401–408 (1986)

    ADS  CAS  Article  Google Scholar 

  13. Chamorro-Pérez, E., Gillet, Ph., Jambon, A., Badro, J. & McMillan, P. Low argon solubility in silicate melts at high pressure. Nature 393, 352–355 (1998)

    ADS  Article  Google Scholar 

  14. Bottinga, Y. & Javoy, M. MORB degassing: bubble growth and ascent. Chem. Geol. 81, 255–270 (1990)

    ADS  CAS  Article  Google Scholar 

  15. Sarda, P. & Graham, D. Mid-ocean ridge popping rocks: implications for degassing at ridge crests. Earth Planet. Sci. Lett. 97, 268–289 (1990)

    ADS  CAS  Article  Google Scholar 

  16. Javoy, M. & Pineau, F. The volatiles record of a “popping” rock from the mid-atlantic ridge at 14 °N: chemical and isotopic composition of gas trapped in the vesicles. Earth Planet. Sci. Lett. 107, 598–611 (1991)

    ADS  CAS  Article  Google Scholar 

  17. Burnard, P., Graham, D. & Turner, G. Vesicle-specific noble gas analyses of ‘popping rock’: implications for primordial noble gases in the Earth. Science 276, 568–571 (1997)

    CAS  Article  Google Scholar 

  18. Graham, D. & Sarda, P. Reply to comment by T.M. Gerlach on ‘Mid-ocean ridge popping rocks: implications for degassing at ridge crests’. Earth Planet. Sci. Lett. 105, 568–573 (1991)

    ADS  Article  Google Scholar 

  19. Moreira, M., Kunz, J. & Allègre, C. Rare gas systematics in popping rock: isotopic and elemental compositions in the upper mantle. Science 279, 1178–1181 (1998)

    ADS  CAS  Article  Google Scholar 

  20. Allègre, C. J., Staudacher, T. & Sarda, P. Rare gas systematics: formation of the atmosphere, evolution and structure of the Earth's mantle. Earth Planet. Sci. Lett. 81, 127–150 (1987)

    ADS  Article  Google Scholar 

  21. Ballentine, C. J., van Keken, P. E., Porcelli, D. & Hauri, E. H. Numerical models, geochemistry and the zero-paradox noble gas mantle. Phil. Trans. R. Soc. Lond. A 360, 2611–2631 (2002)

    ADS  CAS  Article  Google Scholar 

  22. Rigden, S. M., Ahrens, T. J. & Stolper, E. M. Densities of liquid silicates at high pressures. Science 226, 1071–1074 (1984)

    ADS  CAS  Article  Google Scholar 

  23. Gaetani, G. A., Asimow, P. D. & Stolper, E. Determination of the partial molar volume of SiO2 in silicate liquids at elevated pressures and temperatures: a new experimental approach. Geochim. Cosmochim. Acta 62, 2499–2508 (1998)

    ADS  CAS  Article  Google Scholar 

  24. Agee, C. B. & Walker, D. Static compression and olivine flotation of ultrabasic silicate liquid. J. Geophys. Res. 93, 3437–3449 (1988)

    ADS  CAS  Article  Google Scholar 

  25. Kirsten, T. Incorporation of rare gases in solidifying enstatite melts. J. Geophys. Res. 73, 2807–2810 (1968)

    ADS  CAS  Article  Google Scholar 

  26. Shibata, T., Takahashi, E. & Matsuda, J.-I. Solubility of neon, argon, krypton and xenon in binary and ternary silicate systems: a new view on noble gas solubility. Geochim. Cosmochim. Acta 62, 1241–1253 (1998)

    ADS  CAS  Article  Google Scholar 

  27. Carroll, M. R. & Draper, D. S. Noble gases as trace elements in magmatic processes. Chem. Geol. 117, 37–56 (1994)

    ADS  CAS  Article  Google Scholar 

  28. Mourtada-Bonnefoi, C. C. & Laporte, D. Kinetics of bubble nucleation in a rhyolitic melt: an experimental study of the effect of ascent rate. Earth Planet. Sci. Lett. 218, 521–537 (2004)

    ADS  CAS  Article  Google Scholar 

  29. Pan, V., Holloway, J. R. & Hervig, R. L. The pressure and temperature dependence of carbon dioxide solubility in tholeiitic basalt melts. Geochim. Cosmochim. Acta 55, 1587–1595 (1991)

    ADS  CAS  Article  Google Scholar 

Download references


We thank P. Burnard for sharing data and discussions, and P. Richet for discussions and encouragements.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Philippe Sarda.

Ethics declarations

Competing interests

Reprints and permissions information is available at The authors declare no competing financial interests.

Supplementary information

Supplementary Notes

A development of the model in some detail, references to the literature, and a legend for the Supplementary Figure S1. (DOC 264 kb)

Supplementary Figure S1

Two diagrams showing pressure (in kbar) vs. density (in g/cm3) for gases and for various silicate liquids, both using the Carnahan Starling equation of state. (PDF 66 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sarda, P., Guillot, B. Breaking of Henry's law for noble gas and CO2 solubility in silicate melt under pressure. Nature 436, 95–98 (2005).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing