Skip to main content

Thank you for visiting nature.com. 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.

  • Letter
  • Published:

Thermal and electrical conductivity of iron at Earth’s core conditions

Abstract

The Earth acts as a gigantic heat engine driven by the decay of radiogenic isotopes and slow cooling, which gives rise to plate tectonics, volcanoes and mountain building. Another key product is the geomagnetic field, generated in the liquid iron core by a dynamo running on heat released by cooling and freezing (as the solid inner core grows), and on chemical convection (due to light elements expelled from the liquid on freezing). The power supplied to the geodynamo, measured by the heat flux across the core–mantle boundary (CMB), places constraints on Earth’s evolution1. Estimates of CMB heat flux2,3,4,5 depend on properties of iron mixtures under the extreme pressure and temperature conditions in the core, most critically on the thermal and electrical conductivities. These quantities remain poorly known because of inherent experimental and theoretical difficulties. Here we use density functional theory to compute these conductivities in liquid iron mixtures at core conditions from first principles—unlike previous estimates, which relied on extrapolations. The mixtures of iron, oxygen, sulphur and silicon are taken from earlier work6 and fit the seismologically determined core density and inner-core boundary density jump7,8. We find both conductivities to be two to three times higher than estimates in current use. The changes are so large that core thermal histories and power requirements need to be reassessed. New estimates indicate that the adiabatic heat flux is 15 to 16 terawatts at the CMB, higher than present estimates of CMB heat flux based on mantle convection1; the top of the core must be thermally stratified and any convection in the upper core must be driven by chemical convection against the adverse thermal buoyancy or lateral variations in CMB heat flow. Power for the geodynamo is greatly restricted, and future models of mantle evolution will need to incorporate a high CMB heat flux and explain the recent formation of the inner core.

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

Access options

Buy this article

Purchase on Springer Link

Instant access to full article PDF

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Electrical and thermal conductivity of iron at Earth’s outer core conditions.
Figure 2: Stabilizing and destabilizing gradients for three core energetics models.

Similar content being viewed by others

References

  1. Lay, T., Hernlund, J. & Buffett, B. Core-mantle boundary heat flow. Nature Geosci. 1, 25–32 (2008)

    Article  ADS  CAS  Google Scholar 

  2. Labrosse, S., Poirier, J.-P. & Le Mouël, J.-L. On cooling of the Earth’s core. Phys. Earth Planet. Inter. 99, 1–17 (1997)

    Article  ADS  Google Scholar 

  3. Buffett, B., Garnero, E. & Jeanloz, R. Sediments at the top of Earth’s core. Science 290, 1338–1342 (2000)

    Article  ADS  CAS  Google Scholar 

  4. Lister, J. R. & Buffett, B. A. The strength and efficiency of thermal and compositional convection in the geodynamo. Phys. Earth Planet. Inter. 91, 17–30 (1995)

    Article  ADS  Google Scholar 

  5. Gubbins, D., Alfè, D., Masters, T. G. & Price, D. Gross thermodynamics of 2-component core convection. Geophys. J. Int. 157, 1407–1414 (2004)

    Article  ADS  CAS  Google Scholar 

  6. Alfè, D., Gillan, M. J. & Price, G. D. Temperature and composition of the Earth’s core. Contemp. Phys. 48, 63–80 (2007)

    Article  ADS  Google Scholar 

  7. Masters, T. G. & Gubbins, D. On the resolution of density within the Earth. Phys. Earth Planet. Inter. 140, 159–167 (2003)

    Article  ADS  Google Scholar 

  8. Dziewonski, A. M. & Anderson, D. L. Preliminary Reference Earth Model. Phys. Earth Planet. Inter. 25, 297–356 (1981)

    Article  ADS  Google Scholar 

  9. Silvestrelli, P. L., Alavi, A. & Parrinello, M. Electrical conductivity calculation in ab initio simulations of metals: application to liquid sodium. Phys. Rev. B 55, 15515–15522 (1997)

    Article  ADS  CAS  Google Scholar 

  10. Mattsson, T. R. & Desjarlais, M. P. Phase diagram and electrical conductivity of high energy density water from density functional theory. Phys. Rev. Lett. 97, 017801 (2007)

    Article  ADS  Google Scholar 

  11. Pozzo, M., Desjarlais, M. P. & Alfè, D. Electrical and thermal conductivity of liquid sodium from first principles calculations. Phys. Rev. B 84, 054203 (2011)

    Article  ADS  Google Scholar 

  12. Alfè, D., Gillan, M. J. & Price, G. D. The melting curve of iron at the pressures of the Earth’s core conditions. Nature 401, 462–464 (1999)

    Article  ADS  Google Scholar 

  13. Alfè, D. Temperature of the inner-core boundary of the Earth: melting of iron at high pressure from first-principles coexistence simulations. Phys. Rev. B 79, 060101(R) (2009)

    Article  ADS  Google Scholar 

  14. Alfè, D., Pozzo, M. & Desjarlais, M. P. Lattice electrical resistivity of magnetic body-centred cubic iron from first principles calculations. Phys. Rev. B 85, 024102 (2012)

    Article  ADS  Google Scholar 

  15. Bi, Y., Tan, H. & Jing, F. Electrical conductivity of iron under shock compression up to 200 GPa. J. Phys. Condens. Matter 14, 10849–10854 (2002)

    Article  ADS  CAS  Google Scholar 

  16. Keeler, R. N. & Royce, E. B. in Physics of High Energy Density (eds Caldirola, P. & Knoepfel, H. ) 106–125 (Proc. Int. Sch. Phys. Enrico Fermi Vol. 48, 1971)

    Google Scholar 

  17. Stacey, F. D. & Anderson, O. L. Electrical and thermal conductivities of Fe–Ni–Si alloy under core conditions. Phys. Earth Planet. Inter. 124, 153–162 (2001)

    Article  ADS  CAS  Google Scholar 

  18. Hirose, K. Gomi, H. Ohta, K. Labrosse, S. & Hernlund, J. The high conductivity of iron and thermal evolution of the Earth’s core. Mineral. Mag. 75, 1027 (2011)

    Google Scholar 

  19. de Koker, N., Steinle-Neumann, G. & Vlcek, V. Electrical resistivity and thermal conductivity of liquid Fe alloys at high P and T, and heat flux in Earth's core. Proc. Natl Acad. Sci. 109, 4070–4073 (2012)

    Article  ADS  CAS  Google Scholar 

  20. Davies, C. J. & Gubbins, D. A buoyancy profile for the Earth’s core. Geophys. J. Int. 187, 549–563 (2011)

    Article  ADS  Google Scholar 

  21. Olson, P. in Earth’s Core and Lower Mantle (eds Jones, C., Soward, A. & Zhang, K. ) 1–49 (Taylor and Francis, London, 2000)

    Google Scholar 

  22. Nakagawa, T. &. Tackley, P. J. Lateral variations in CMB heat flux and deep mantle seismic velocity caused by a thermal-chemical-phase boundary layer in 3D spherical convection. Earth Planet. Sci. Lett. 271, 348–358 (2008)

    Article  ADS  CAS  Google Scholar 

  23. Jackson, A., Jonkers, A. R. T. & Walker, M. R. Four centuries of geomagnetic secular variation from historical records. Phil. Trans. R. Soc. Lond. B 358, 957–990 (2000)

    Article  ADS  CAS  Google Scholar 

  24. Gubbins, D. in Encyclopedia of Geomagnetism and Paleomagnetism (eds Gubbins, D. & Herrero-Bervera, E. ) 287–300 (Springer, 2007)

    Book  Google Scholar 

  25. Davies, G. Topography: a robust constraint on mantle fluxes. Chem. Geol. 145, 479–489 (1998)

    Article  ADS  CAS  Google Scholar 

  26. Davies, G. Mantle regulation of core cooling: a geodynamo without core radioactivity? Phys. Earth Planet. Inter. 160, 215–229 (2007)

    Article  ADS  CAS  Google Scholar 

  27. McDonough, W. in Treatise on Geochemistry Vol. 2 (ed. Carlson, R. W. ) 547–568 (Elsevier, 2003)

    Book  Google Scholar 

  28. Kresse, G. & Furthmuller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996)

    Article  CAS  Google Scholar 

  29. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994)

    Article  ADS  Google Scholar 

  30. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999)

    Article  ADS  CAS  Google Scholar 

  31. Wang, Y. & Perdew, J. P. Correlation hole of the spin-polarized electron gas, with exact small-wave-vector and high-density scaling. Phys. Rev. B 44, 13298–13307 (1991)

    Article  ADS  CAS  Google Scholar 

  32. Desjarlais, M. P., Kress, J. D. & Collins, L. A. Electrical conductivity for warm, dense aluminum plasmas and liquids. Phys. Rev. E 66, 025401(R) (2002)

    Article  ADS  Google Scholar 

  33. Alfè, D. Ab initio molecular dynamics, a simple algorithm for charge extrapolation. Comput. Phys. Commun. 118, 31–33 (1999)

    Article  ADS  Google Scholar 

  34. Buffett, B. A. Estimates of heat flow in the deep mantle based on the power requirements for the geodynamo. Geophys. Res. Lett. 29, 1566–1569 (2002)

    Article  ADS  Google Scholar 

  35. Kuang, W. & Bloxham, J. An Earth-like numerical dynamo model. Nature 389, 371–374 (1997)

    Article  ADS  CAS  Google Scholar 

  36. Gubbins, D., Alfè, D., Masters, T. G., Price, D. & Gillan, M. J. Can the Earth’s dynamo run on heat alone? Geophys. J. Int. 155, 609–622 (2003)

    Article  ADS  Google Scholar 

  37. Anufriev, A. P., Jones, C. A. & Soward, A. M. The Boussinesq and anelastic liquid approximations for convection in the Earth’s core. Phys. Earth Planet. Inter. 152, 163–190 (2005)

    Article  ADS  Google Scholar 

  38. Gubbins, D. & Roberts, P. H. in Geomagnetism (ed. Jacobs, J. A. ) 30–32 (Academic, 1987)

    Google Scholar 

Download references

Acknowledgements

D.G. is supported by CSEDI grant EAR1065597 from the National Science Foundation. C.D. is supported by a Natural Environment Research Council personal fellowship, NE/H01571X/1. M.P. is supported by NERC grant NE/H02462X/1 to D.A. Calculations were performed on the UK national facility HECToR.

Author information

Authors and Affiliations

Authors

Contributions

D.A. and D.G. designed the project. M.P. and D.A. performed the first principles calculations. C.D. and D.G. performed the thermal history and core stratification calculations. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Dario Alfè.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Tables

This file contains Supplementary Tables 1-3. (PDF 203 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pozzo, M., Davies, C., Gubbins, D. et al. Thermal and electrical conductivity of iron at Earth’s core conditions. Nature 485, 355–358 (2012). https://doi.org/10.1038/nature11031

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature11031

This article is cited by

Comments

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.

Search

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