This page is about the physics of the Earth's core.

The core of the Earth accounts for about 30 % of the total mass of our planet, the inner solid core is crystallizing from the liquid outer core, and the heat released flows to the surface, driving all the living geological processes of the Earth, including plate tectonics, volcanism and earthquakes. The cystallization of the inner core is also responsible for compositional convection in the liquid core, that is the engine which generates the Earth's magnetic field, shielding us from the lethal solar wind. So, a sound knowledge of the core is of fundamental importance, yet, it is one of the most difficult things to study, and its properties are poorly constrained. For example, we know that it is mainly made by iron, but it can't be pure iron, because its density is too low. So it must contain some light element, and the most likely candidates are sulphur, oxygen, carbon and silicon, but the real composition of the Earth's core remains one of the major unsolved problems. The density and the pressure are known quite accurately (within a percent), but the temperature is unknown, with estimates ranging from 4000 to 8000 K.

We have tackled some of these problems
using first principles techniques, and a report on our
recent work just published in the journal Nature
was picked up by the media, and there were interviews on Channel 4 News
and the Today programme. There was even a half-page item on our work in
the

Daily
Mirror, and on the BBC
on-line web page.

More recently, we participated to the BBC Radio 4 science program "The Material World".

See a recent poster.

The aim of our work is to use ab initio techniques to investigate the properties of liquid and solid iron (both pure and alloyed with light elements) under the conditions of the Earth's deep interior.

Some of the work already done includes:

- The viscosity of pure Iron and Iron-Sulphur under Earth's core conditions. We have found that the viscosity of liquid iron is about 13 mPa s, little different from tipical viscosities of liquid metals under ambient conditions. Sulphur impurities in the concentration of about 20 % hardly change the properties of the liquid, and the viscosity in particular is approximatively the same. Initially, the viscosity has been calculated using the Stokes-Einstein relation, which connects the viscosity of a liquid with the diffusion coefficient. The latter has been calculated using first-principles molecular dynamics simulations. This relation is exact when applyed to the diffusion of macroscopic objects, but it is only approximate when applyed to atoms. However, we have later calculated the viscosity directly, using the Green-Kubo relation, which connect the shear viscosity to the integral of the average of the stress autocorrelation function (see figures on the right). We obtained the value 9 ± 2 mPa s, which is not very far from the one obtained using the Stokes-Einstein relation, thus confirming its validity.

- Ab-initio investigations of the structural and dynamical properties of Fe, Fe/S and Fe/O under Earth's core conditions.

- Ab-initio free-energy calculations to determine the melting point of iron as a function of pressure, in the range 50-350 GPa. The condition for two phases to be in thermal equilibrium at a given temperature T and pressure P is that their Gibbs free energies G(P,T) are equal. To determine the melting temperature T at any pressure we calculate G for the solid and liquid phases as a function of T and determine when they are equal. In fact, we calculate the Helmhotz free energy F(V,T), and G through its definition G = F + PV. To calculate the free energy of the liquid we used the techniques called `thermodyanics integration', starting from a very simple reference system, which is the sum of inverse power pair-potentials. For the solid, we decompose the free energy in three parts. The first is the free energy of the perfect, non-vibrating crystal, which is straightforward to compute. The second part is the harmonic free energy, which we calculate by computing the phonon frequencies in the whole Brillouin zone. The third part is the anharmonic contribution, which we calculate again using thermodynamics integration. This time the reference system is a combination of inverse powers and ab initio harmonic. The resulting melting curve is compared with the experiments here on the right.

- Since we know the free energies we can also calculate the thermodynamics of solid(h.c.p.) and liquid iron.

We have recently used our free energy calculation techniques to put a constraint on the composition and temperature of the Earth's core. Among the possible light elements we consider Sulphur, Silicon and Oxygen.

At Inner Core Boundary solid and liquid
are in equilibrium, therefore the chemical potential of all the elements
must be equal in the two phases. This fixes the ratio of concentration
of the elements in the liquid and in the solid, which in turn fixes the
densities. A comparison with seismological data allows us to rule
out all binary mixtures, i.e. the Core __cannot__ be made of
Fe/S,
Fe/Si
or
Fe/O. The reason
is that S and
Si
do not partition enough between solid and liquid, the concentration in
the solid is almost equal to the concentration in the liquid, so the density
jump at ICB cannot be reproduced. Oxygen
instead partitions too much, very little of it goes into the solid and
again the density jump cannot be reproduced.

The composition of the Earth's core must be at least a ternary mixture.

Assuming that the presence of one impurity does not affect the chemical potential of a different element we suggest the following composition for the Earth's core:

Composition at ICB

Solid | Liquid | |

Sulphur/Silicon | 8.5 +- 2.5 % | 10.0 +- 2.5 % |

Oxygen | 0.2 +- 0.1 % | 8.0 +- 2.5 % |

The partitioning of the light elements implies a depression of the melting point with respect to that of pure Iron, and we estimate this depression to be about 600-700 K.

The first part of this work has been published
in Nature
and GRL
recently.

References:

1. G. A. de Wijs, G. Kresse, L. Vocadlo, D. Dobson, D. Alfè, M. J. Gillan, G. D. Price, "The viscosity of liquid iron under Earth's core conditions", Nature, 392 , 805-807 (1998).

2. D. Alfè and M. J. Gillan, "First principles simulations of liquid Fe-S under Earth's core conditions", Physical Review B, 58, 8248-8256 (1998).

3. D. Alfè and M. J. Gillan, "The first principles calculation of transport coefficients", Physical Review Letter, 81, 5161-5164 (1998).

4. D. Alfè, G. D. Price, and M. J. Gillan, "Oxygen in the Earth's core: a first principles study", Physics ofthe Earth and Planetary Interiors, 110, 191-210 (1999).

5. D. Alfè, "Ab-initio molecular dynamics, a simple algorithm for charge extrapolation, Computer PhysicsCommunications, 118, 31-33 (1999).

6. L. Vocadlo, D. Alfè, J. Brodholt, M. J. Gillan, andG. D. Price, "The structure of Iron under the conditions of the Earth's Inner Core, Geophysical Research Letters, 26 , 1231-1235 (1999).

7. D. Alfè, G. D.
Price, and M. J. Gillan, "Melting curve of Iron at Earth's core pressures
from ab-initio calculations",
Nature,
401, 462-464 (1999).

(News
& Views).

8. L. Vocadlo, D. Alfè , J. Brodholt, M. J. Gillan, and G. D. Price, "Ab-initio free energy calculations on the polymorphs of iron at core conditions", Physics of the Earth and Planetary Interiors, 117, 123-137 (2000).

9. D.Alfè, G. A. de Wijs, G. Kresse and M. J. Gillan, "Recent developments in ab-initio thermodynamics", International Journal of Quantum Chemistry, 77, 871-879 (2000).

10. D. Alfè, G. Kresse and M. J. Gillan, "Structure and dynamics of liquid Iron under Earth's core conditions", Physical Review B, 61, 132-142 (2000)

11. D. Alfè, G. D. Price, and M. J. Gillan, "Thermodynamics of hexagonal close packed iron under Earth's core conditions", Physical Review B, submitted, preprint.

12. D. Alfè, M. J. Gillan, and G. D. Price, "Constraints on the composition of the Earth's core from ab-initio calculations", Nature, 405, 172-175 (2000).

13. D. Alfè, G. D.
Price, and M. J. Gillan, "Thermodynamic stability of Fe/O solid solution
at inner-core conditions", Geophysical
Research Letters, 27, 2417-2420 (2000).

And if you read up to here you deserve to see a beautiful picture...