Self-consistent thermodynamic description of silicate liquids, with application to shock melting of MgO periclase and MgSiO 3 perovskite

We develop a self-consistent thermodynamic description of silicate liquids applicable across the entire mantle pressure and temperature regime. The description combines the finite strain free energy expansion with an account of the temperature dependence of liquid properties into a single fundamental relation, while honouring the expected limiting behaviour at large volume and high temperature. We find that the fundamental relation describes well previous experimental and theoretical results for liquid MgO, MgSiO 3 , Mg 2 SiO 4 and SiO 2 . We apply the description to calculate melting curves and Hugoniots of solid and liquid MgO and MgSiO 3 . For periclase, we find a melting temperature at the core–mantle boundary (CMB) of 7810 ± 160 K , with the solid Hugoniot crossing the melting curve at 375 GPa, 9580 K , and the liquid Hugoniot crossing at 470 GPa, 9870 K . For complete shock melting of periclase we predict a density increase of 0.14 g cm −3 and a sound speed decrease of 2.2 km s −1 . For perovskite, we find a melting temperature at the CMB of 5100 ± 100 K with the perovskite section of the enstatite Hugoniot crossing the melting curve at 150 GPa, 5190 K , and the liquid Hugoniot crossing at 220 GPa, 5520 K . For complete shock melting of perovskite along the enstatite principal Hugoniot, we predict a density increase of 0.10 g cm −3 , with a sound speed decrease of 2.6 km s −1 .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75103/1/j.1365-246X.2009.04142.x.pd

Liquid State Physics of the MgO-SiO2 System at Deep Mantle Pressures.

As the primary medium through which planetary differentiation occurs, silicate liquids are key in the study of the thermal and chemical evolution of Earth. First principles molecular dynamics simulations were used to study the liquid state physics of the MgO - SiO2 join at pressure and temperature conditions relevant to the deep interiors of Earth-like planets, with special focus on the variation of liquid state thermodynamics and structure with pressure, temperature and composition. We find the structure of liquids to change continuously upon compression, and to differ markedly from that of the respective isochemical crystalline polymorphs. Si-O coordination increases from four to six upon two-fold compression in all compositions considered, with the increase strongly delayed in pure silica. Changes in liquid structure is expressed in the liquid state thermodynamic properties. A density crossover along the forsterite melting curve is found within the stability field of the mineral, a feature which a melting curve computed through the Lindemann criterion from the mean squared atomic displacements in forsterite is unable to reproduce. Composition dependent structural differences within the liquid are expressed as a liquid immiscibility field at low pressure in high silica compositions. Using our first principles molecular dynamics results, we develop a self-consistent thermodynamic description of liquid state thermodynamics, which also accounts for the thermal electronic contribution to the free energy, relevant to silicate liquids over a large range of pressures and temperature. With liquid state thermodynamics thus self-consistently constrained, we investigate the high pressure melting of MgO periclase and MgSiO3 perovskite. By calculating theoretical solid and liquid Hugoniot loci, we predict the changes in density and sound velocity which would be expected during shock melting of periclase and enstatite. We also apply the thermodynamic description to the thermodynamics of mixing along the extent of the binary. At low pressure the enthalpy of mixing is notably pressure dependent, primarily due to the disappearance of a maximum at high silica compositions with an increase in pressure. The structural mechanism responsible for liquid immiscibility is identified, and found to be stable only at low pressure.Ph.D.GeologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60828/1/dekoker_1.pd

The effects of lithospheric thickness and density structure on Earth's stress field

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/89572/1/j.1365-246X.2011.05248.x.pd