The conduction of heat through minerals and melts at extreme pressures and temperatures is of central importance to the evolution and dynamics of planets. In the cooling Earth’s core, the thermal conductivity of iron alloys defines the adiabatic heat flux and therefore the thermal and compositional energy available to support the production of Earth’s magnetic field via dynamo action1,2,3. Attempts to describe thermal transport in Earth’s core have been problematic, with predictions of high thermal conductivity4,5,6,7 at odds with traditional geophysical models and direct evidence for a primordial magnetic field in the rock record8,9,10. Measurements of core heat transport are needed to resolve this difference. Here we present direct measurements of the thermal conductivity of solid iron at pressure and temperature conditions relevant to the cores of Mercury-sized to Earth-sized planets, using a dynamically laser-heated diamond-anvil cell11,12. Our measurements place the thermal conductivity of Earth’s core near the low end of previous estimates, at 18–44 watts per metre per kelvin. The result is in agreement with palaeomagnetic measurements10 indicating that Earth’s geodynamo has persisted since the beginning of Earth’s history, and allows for a solid inner core as old as the dynamo.
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Labrosse, S. Thermal and magnetic evolution of the Earth’s core. Phys. Earth Planet. Inter. 140, 127–143 (2003)
Stacey, F. D. & Loper, D. E. A revised estimate of the conductivity of iron alloy at high pressure and implications for the core energy balance. Phys. Earth Planet. Inter. 161, 13–18 (2007)
Nimmo, F. in Treatise on Geophysics 2nd edn (ed. Schubert, G. ) 27–55, 201–219 (Elsevier, 2015)
Sha, X. & Cohen, R. First-principles studies of electrical resistivity of iron under pressure. J. Phys. Condens. Matter 23, 075401 (2011)
Gomi, H. et al. The high conductivity of iron and thermal evolution of the Earth’s core. Phys. Earth Planet. Inter. 224, 88–103 (2013)
Pozzo, M., Davies, C., Gubbins, D. & Alfe, D. Thermal and electrical conductivity of iron at Earth’s core conditions. Nature 485, 355–358 (2012)
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. USA 109, 4070–4073 (2012)
Olson, P. The new core paradox. Science 342, 431–432 (2013)
Nimmo, F. in Treatise on Geophysics (ed. Schubert, G. ) 31–65, 217–241 (Elsevier, 2007)
Tarduno, J. A., Cottrell, R. D., Davis, W. J., Nimmo, F. & Bono, R. K. A Hadean to Paleoarchean geodynamo recorded by single zircon crystals. Science 349, 521–524 (2015)
McWilliams, R. S., Konôpková, Z. & Goncharov, A. F. A flash heating method for measuring thermal conductivity at high pressure and temperature: application to Pt. Phys. Earth Planet. Inter. 247, 17–26 (2015)
McWilliams, R. S., Dalton, D. A., Konôpková, Z., Mahmood, M. F. & Goncharov, A. F. Opacity and conductivity measurements in noble gases at conditions of planetary and stellar interiors. Proc. Natl Acad. Sci. USA 112, 7925–7930 (2015)
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)
Seagle, C. T., Cottrell, E., Fei, Y. W., Hummer, D. R. & Prakapenka, V. B. Electrical and thermal transport properties of iron and iron-silicon alloy at high pressure. Geophys. Res. Lett. 40, 5377–5381 (2013)
Bi, Y., Tan, H. & Jing, F. Electrical conductivity of iron under shock compression up to 200 GPa. J. Phys. Condens. Matter 14, 10849 (2002)
Keeler, R. N. & Royce, E. B. in Physics of High Energy Density Vol. 48 (eds Caldirola, P. & Knoepfel, H. ) 106–125 (Academic Press, 1971)
Franz, R. & Wiedemann, G. Ueber die Wärme-Leitungsfähigkeit der Metalle. Ann. Phys. 165, 497–531 (1853)
Anzellini, S., Dewaele, A., Mezouar, M., Loubeyre, P. & Morard, G. Melting of iron at Earth’s inner core boundary based on fast X-ray diffraction. Science 340, 464–466 (2013)
Boehler, R. Temperatures in the Earth’s core from melting-point measurements of iron at high static pressures. Nature 363, 534–536 (1993)
Komabayashi, T., Fei, Y., Meng, Y. & Prakapenka, V. In-situ X-ray diffraction measurements of the γ-ε transition boundary of iron in an internally-heated diamond anvil cell. Earth Planet. Sci. Lett. 282, 252–257 (2009)
Deng, L., Seagle, C., Fei, Y. & Shahar, A. High pressure and temperature electrical resistivity of iron and implications for planetary cores. Geophys. Res. Lett. 40, 33–37 (2013)
Jackson, J. M. et al. Melting of compressed iron by monitoring atomic dynamics. Earth Planet. Sci. Lett. 362, 143–150 (2013)
Rivoldini, A., Van Hoolst, T. & Verhoeven, O. The interior structure of Mercury and its core sulfur content. Icarus 201, 12–30 (2009)
Ho, C. Y., Powell, R. W. & Liley, P. E. Thermal conductivity of the elements. J. Phys. Chem. Ref. Data 1, 279–422 (1972)
Hauck, S. A., Dombard, A. J., Phillips, R. J. & Solomon, S. C. Internal and tectonic evolution of Mercury. Earth Planet. Sci. Lett. 222, 713–728 (2004)
Konôpková, Z., Lazor, P., Goncharov, A. F. & Struzhkin, V. V. Thermal conductivity of hcp iron at high pressure and temperature. High Press. Res. 31, 228–236 (2011)
Dubrovinsky, L. S., Saxena, S. K., Tutti, F., Rekhi, S. & LeBehan, T. In situ X-ray study of thermal expansion and phase transition of iron at multimegabar pressure. Phys. Rev. Lett. 84, 1720–1723 (2000)
Secco, R. A. & Schloessin, H. H. The electrical resistivity of solid and liquid Fe at pressures up to 7 GPa. J. Geophys. Res. Solid Earth 94, 5887–5894 (1989)
Nimmo, F. & Stevenson, D. J. Influence of early plate tectonics on the thermal evolution and magnetic field of Mars. J. Geophys. Res. Planets 105, 11969–11979 (2000)
Montoya, J. A. & Goncharov, A. F. Finite element calculations of the time dependent thermal fluxes in the laser-heated diamond anvil cell. J. Appl. Phys. 111, 112617 (2012)
Johannsen, P. G. Refractive index of the alkali halides. 1. Constant joint density of states model. Phys. Rev. B 55, 6856–6864 (1997)
Grimsditch, M., Letoullec, R., Polian, A. & Gauthier, M. Refractive index determination in diamond anvil cells: results for argon. J. Appl. Phys. 60, 3479–3481 (1986)
Chen, B. et al. Elasticity, strength, and refractive index of argon at high pressures. Phys. Rev. B 81, 144110 (2010)
Dewaele, A. et al. Quasihydrostatic equation of state of iron above 2 Mbar. Phys. Rev. Lett. 97, 215504 (2006)
Sommerfeld, A. Zur Elektronentheorie der Metalle auf Grund der Fermischen Statistik. Z. Phys. 47, 1–32 (1928)
Parker, W. J., Jenkins, R. J., Abbott, G. L. & Butler, C. P. Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J. Appl. Phys. 32, 1679 (1961)
Tateno, S., Hirose, K., Ohishi, Y. & Tatsumi, Y. The structure of iron in Earth’s inner core. Science 330, 359–361 (2010)
Shen, G., Prakapenka, V. B., Rivers, M. L. & Sutton, S. R. Structure of liquid iron at pressures up to 58 GPa. Phys. Rev. Lett. 92, 185701 (2004)
Goncharov, A. F. et al. X-ray diffraction in the pulsed laser heated diamond anvil cell. Rev. Sci. Instrum. 81, 113902 (2010)
Ross, R. G., Andersson, P., Sundqvist, B. & Backstrom, G. Thermal conductivity of solids and liquids under pressure. Rep. Prog. Phys. 47, 1347 (1984)
Bohlin, L. Thermal conduction of metals at high pressure. Solid State Commun. 19, 389–390 (1976)
Sharma, S. K. Debye temperature of hcp iron at extreme compression. Solid State Commun. 149, 2207–2209 (2009)
Dubrovinsky, L. S., Saxena, S. K., Dubrovinskaia, N. A., Rekhi, S. & Le Bihan, T. Gruneisen parameter of ε-iron up to 300 GPa from in-situ X-ray study. Am. Mineral. 85, 386–389 (2000)
Van Zytveld, J. Electrical resistivities of liquid transition metals. J. Phys. Coll. 41, C8-503-C8-506 (1980)
French, M. & Mattsson, T. R. Thermoelectric transport properties of molybdenum from ab-initio simulations. Phys. Rev. B 90, 165113 (2014)
Kittel, C. Introduction to Solid State Physics 8th edn (John Wiley & Sons, 2005)
Panero, W. R. & Jeanloz, R. Temperature gradients in the laser-heated diamond anvil cell. J. Geophys. Res. Solid Earth 106, 6493–6498 (2001)
Kiefer, B. & Duffy, T. S. Finite element simulations of the laser-heated diamond-anvil cell. J. Appl. Phys. 97, 114902 (2005)
Goncharov, A. F. et al. Thermal conductivity of argon at high pressures and high temperatures. J. Appl. Phys. 111, 112609 (2012)
Beck, P. et al. Measurement of thermal diffusivity at high pressure using a transient heating technique. Appl. Phys. Lett. 91, 181914 (2007)
Yamazaki, D. et al. P-V-T equation of state for ε-iron up to 80 GPa and 1900 K using the Kawai-type high pressure apparatus equipped with sintered diamond anvils. Geophys. Res. Lett. 39, L20308 (2012)
Hirose, K., Labrosse, S. & Hernlund, J. Composition and state of the core. Annu. Rev. Earth Planet. Sci. 41, 657–691 (2013)
We acknowledge experimental assistance from H. Marquardt. This work was supported by the NSF (grant numbers DMR-1039807, EAR-1015239, EAR-1520648 and EAR/IF-1128867), the Army Research Office (grant 56122-CH-H), the Carnegie Institution of Washington, the National Natural Science Foundation of China (grant number 21473211), the Chinese Academy of Science (grant number YZ201524), the University of Edinburgh, and the British Council Researcher Links Programme. Portions of this research were carried out at the light source Petra III at DESY, a member of the Helmholtz Association (HGF).
The authors declare no competing financial interests.
Extended data figures and tables
a, Graph of the electrical conductivity5 as a function of temperature of ε Fe at 65 GPa and model fit (to equation (7)). b, Thermal conductivity temperature dependence at 112 GPa. The model fit (to equation (2), solid line) and a 20% uncertainty envelope are in blue; the model fit without linear term (to equation (10)) is a dashed blue line. Present data are solid circles and data derived from prior electrical resistivity measurements5,14,15 are open symbols (see Fig. 3). The red band is the minimum thermal conductivity assuming resistivity saturation5. c, Electrical resistivity at several pressures, for multiple phases at 15 GPa (blue)21, and the ε phase at 65 GPa (red)5 and 112 GPa (this study, black).
Extended Data Figure 2 Comparison between measurements and models for different values of thermal conductivity.
Data for pulsed and opposite sides of the foil are dots; the larger temperature excursion is on the pulsed side. Green, magenta and cyan curves are simulations with different values of sample k, all other parameters being held constant. The data sets at 112 GPa (a) and 130 GPa (b) have been measured using 3-μs and 10-μs sweep windows, respectively.
Extended Data Figure 3 Tests of the sensitivity of finite-element model results to input parameters for an example run at 112 GPa.
This experiment shows a large amplitude of temperature modulation that accentuates the effects of parameter changes. A best-fit value of k = 30 W m−1 K−1, obtained using parameters listed in Extended Data Table 1, is obtained from these model fits unless stated otherwise. a, Effect of heat capacity of the Ar pressure medium. Uncertainty in medium CP has no effect on k of the sample. b, Effect of heat capacity of the sample. Temperature profiles for two values of CP of Fe (500 J kg−1 K−1 and 700 J kg−1 K−1) indicate that results are only weakly affected by the uncertainty in CP for Fe. c, Change in the thermal conductivity value of diamond anvils from 1,500 W m−1 K−1 to 2,000 W m−1 K−1 requires an increase in thermal conductivity of the sample from 30 W m−1 K−1 to 31 W m−1 K−1. d, Effect of using a T-dependent k of the medium. After ref. 49, a dependence k(T) = k300(300/T)m is used, where k300 is the 300-K conductivity, T is in kelvin, and m is an exponent (of order 1); k300 (300 W m−1 K−1) is extrapolated from prior results at lower pressure49 and m (0.7) is fitted to the present data. No change in sample k is indicated using this or any other k(T) model we tested for the media. e, Laser beam radius change of ±13% does not affect the temperature noticeably. f, A sample thinner by 23% (reduced from 2.6 μm to 2.0 μm) would require a lower sample k of 22 W m−1 K−1. g, A sample thicker by 15% (increased from 2.6 μm to 3.0 μm) would require an increased sample k of 37 W m−1 K−1. h, The insulation layer was decreased on both sides by 38%, from 1.6 μm to 1.0 μm. Sample k had to increase to 39 W m−1 K−1. i, The insulation layer was increased on both sides by 25%, from 1.6 μm to 2.0 μm. Sample k had to decrease to 27 W m−1 K−1. j, Effect of including T dependence of sample k in models. The temperature profile calculated using our global fit at 112 GPa (equation (2)) is shown as a magenta line; this dependence scaled within its uncertainty (reduced by a factor of 0.83) to improve the fit is shown as a cyan line. The resulting sample k varies between 24 W m−1 K−1 and 35 W m−1 K−1 in the T range of the experiment; the estimate assuming constant sample k is the average of these values.
Extended Data Figure 4 Comparison of data on Fe and Pt at 48 GPa for an identical sample configuration.
The data clearly show slower propagation of heat across the Fe foil compared to Pt (ref. 11), as given by the half-rise time τ. This observation directly shows that thermal diffusivity κ = (k/ρCP) of Fe is much less than Pt, since11,36 κ ∝ 1/τ. Similarly, the smaller amplitude of the perturbation upon opposite surface arrival indicates a smaller k in Fe than in Pt.
Extended Data Figure 5 Comparison between manual and automatic optimization results for an experiment at 130 GPa.
The manual approach, used as our primary fitting method, was based on an adjustment of model parameters by hand within a precision of ~5 W m−1 K−1, giving k = 45 W m−1 K−1 and kAr = 60 W m−1 K−1 as the best fit. The automatic result is the best fit based on a Levenberg–Marquardt least-squares minimization of model parameters, yielding k = 38.6 W m−1 K−1 and kAr = 50.4 W m−1 K−1. The automatic optimization obtained a better least-squares fit (χ2 improved by 23%); however, the difference in k is not statistically significant.
Extended Data Figure 6 Monte Carlo analysis of error coupling in thickness uncertainties and effect on thermal conductivities, for the 130-GPa data set shown in Extended Data Fig. 5.
a, Histogram showing randomly sampled thicknesses (upper and lower medium, and foil) in Gaussian probability distributions with standard deviation 30%. b, Thermal conductivities for Ar and Fe for 64 samples. The greyscale refers to the value of the coupler thickness, showing the correlation between high values for k and thicker coupler. The results of fits shown in Extended Data Fig. 5 are blue and red triangles, while the mean and one standard deviation found from the spread of sampled thermal conductivities is the orange triangle. c and d are histograms showing the distribution of thermal conductivities in b.
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Konôpková, Z., McWilliams, R., Gómez-Pérez, N. et al. Direct measurement of thermal conductivity in solid iron at planetary core conditions. Nature 534, 99–101 (2016). https://doi.org/10.1038/nature18009
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