Electrical conductivity of SiO ₂ at extreme conditions and planetary dynamos

Abstract

Ab intio molecular dynamics simulations show that the electrical conductivity of liquid SiO 2 is semimetallic at the conditions of the deep molten mantle of early Earth and super-Earths, raising the possibility of silicate dynamos in these bodies. Whereas the electrical conductivity increases uniformly with increasing temperature, it depends nonmonotonically on compression. At very high pressure, the electrical conductivity decreases on compression, opposite to the behavior of many materials. We show that this behavior is caused by a novel compression mechanism: the development of broken charge ordering, and its influence on the electronic band gap.high pressure | Earth's mantle | density functional theory | silicate liquids | electrical conductivity P lanetary magnetic fields are produced by a dynamo process via fluid motions in a large rotating body of electrically conducting fluid within the planet's interior. In present-day Earth, the liquid portion of the iron-rich core produces the magnetic field. Early in Earth's history and before the inner core began to grow, the core may not have been able to cool sufficiently rapidly to sustain a dynamo (1). However, the rock record contains evidence for an ancient field of similar intensity to today's field within the first few 100 Ma of Earth's history (2). What caused this early magnetic field is still unknown.Earth is thought to have been largely or completely molten early in its history (3). While the shallow portions of the magma ocean cooled quickly (4), a basal magma ocean, separated from the surface by a crystallizing layer, may have survived for a billion years or more (5). Could the basal magma ocean have produced a magnetic field? While a variety of different materials produce planetary magnetic fields, including iron, hydrogen, and ice, silicate dynamos are so far unknown (6).A key uncertainty is the electrical conductivity σ of silicate liquid at the pressure-temperature conditions of the basal magma ocean (100 GPa, 5,000 K). The conductivity must be sufficiently high for the dynamo process to operate. Recent models indicate that σ > 10 3 S·m −1 to 10 4 S·m −1 is required (7). The possibility of silicate dynamos is not only relevant to early Earth. Silicates appear to be the primary constituents of many superEarth exoplanets. These planets may have hotter interiors that cool more slowly than Earth and may contain larger and longerlived basal magma oceans, so that Super-Earths may also have silicate dynamos. The conditions at the base of a 10-Earthmass Super-Earth mantle are expected to be 1,000 GPa and 13,000 K (8).Near ambient pressure, the electrical conductivity of silicate liquids is far too small to support dynamo activity, and the dominant charge carriers are ions (9). However, experimental evidence suggests that the electrical conductivity of silicate liquids may be much greater at high pressure and temperature and that the dominant charge carriers may be electrons. Oxide liquids are found to become optically reflective along the Hugoniot at press...

A silicate dynamo in the early Earth

“…The electronic density of states also explains why the conductivity of the spin-polarized system is slightly less than that of the non-spin-polarized system: magnetism splits up-and down-spin iron 3d states, reducing the density of states at the Fermi level. While there are no experimental measurements of the electrical conductivity of silicate liquids at basal magma ocean conditions, we have shown that our approach yields results that are in good agreement with available experimental data at high pressure including the optical reflectivity of silica liquid and the electrical conductivity of crystalline (Mg,Fe)O 10,11 .…”

“…Sampling the Brillouin zone at the Gamma point and a basis-set energy cutoff of 500 eV were found to be sufficient to converge energy and pressure to within 2 meV/atom and 0.2 GPa, respectively. Our previous studies 10,11 indicate that our simulations are well converged with respect to the number of atoms: in the case of SiO 2 , simulations with 96 and 144 atoms did not differ significantly in the value of σ, while in the case of (Mg,Fe)O, differences in σ between simulations containing 128, 256, and 512 atoms were less than 10%.…”

“…2). The electrical conductivity of the silicate liquid is intermediate to that of SiO 2 liquid 11,14,15 and (Mg,Fe)O liquid 10 over the range of temperature and pressure that we have investigated. The conductivity of the silicate liquid is greater than that of SiO 2 because of the role of iron.…”

“…Here we perform first principles molecular dynamics simulations of a silicate liquid that closely approximates the composition of the bulk silicate Earth and includes the six most abundant oxide components; the size of our simulation is 1129 atoms (see Methods). The simulations and the computation of the electrical conductivity closely follow our previous work on the SiO 2 and (Mg,Fe)O systems 10,11 (see Methods). Briefly, we compute the electronic contribution to the electrical conductivity with the Kubo-Greenwood formula 12 and the ionic conductivity from the electric current autocorrelation function 13 .…”

Probing space to understand Earth

“…Unresolved questions about the lunar dynamo also prompted research into dynamos generated within basal magma oceans 37 (layers of molten silicates immediately above the core-mantle boundary), as has been proposed for the [38][39][40][41] . For example, core convection in Earth's Moon may provide insufficient energy to sustain a lunar dynamo for the duration and at the intensities indicated by palaeomagnetic data 42 .…”