Stixrude receives James B. Macelwane Medal

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95034/1/eost12216.pd

Thermodynamics of mantle minerals – I. Physical properties

We present a theory for the computation of phase equilibria and physical properties of multicomponent assemblages relevant to the mantle of the Earth. The theory differs from previous treatments in being thermodynamically self-consistent: the theory is based on the concept of fundamental thermodynamic relations appropriately generalized to anisotropic strain and in encompassing elasticity in addition to the usual isotropic thermodynamic properties. In this first paper, we present the development of the theory, discuss its scope, and focus on its application to physical properties of mantle phases at elevated pressure and temperature including the equation of state, thermochemical properties and the elastic wave velocities. We find that the Eulerian finite strain formulation captures the variation of the elastic moduli with compression. The variation of the vibrational frequencies with compression is also cast as a Taylor series expansion in the Eulerian finite strain, the appropriate volume derivative of which leads to an expression for the GrÜneisen parameter that agrees well with results from first principles theory. For isotropic materials, the theory contains nine material-specific parameters: the values at ambient conditions of the Helmholtz free energy, volume, bulk and shear moduli, their pressure derivatives, an effective Debye temperature, its first and second logarithmic volume derivatives (Γ 0 , q 0 ) , and the shear strain derivative of Γ. We present and discuss in some detail the results of a global inversion of a wide variety of experimental data and first principles theoretical results, supplemented by systematic relations, for the values of these parameters for 31 mantle species. Among our findings is that the value of q is likely to be significantly greater than unity for most mantle species. We apply the theory to the computation of the shear wave velocity, and temperature and compositional (Fe content) derivatives at relevant mantle pressure temperature conditions. Among the patterns that emerge is that garnet is anomalous in being remarkably insensitive to iron content or temperature as compared with other mantle phases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73485/1/j.1365-246X.2005.02642.x.pd

Thermal and Tidal Evolution of Ice Giants with Growing Frozen Cores: The Case of Neptune

Abstract: The contrasting internal luminosity of Uranus and Neptune present a challenge to our understanding of the origin and evolution of these bodies, as well as extra-solar ice giants. The thermal evolution of Neptune is known to be nearly consistent with an entirely fluid interior, but this is not a unique solution, and does not account for the tidal dissipation required by the migration of its moons. We examine a model that has been previously shown to explain the thermal and tidal evolution of Uranus: one that features a growing, frozen core. The core traps heat in the interior, affecting the cooling time scale, and provides a source of tidal dissipation. We review the growing, frozen core model, and the computation of thermal and tidal evolution. We then apply this model to Neptune. We find that the growing frozen core model can account for the observed internal luminosity of Neptune and the migration of its moons, in the form of resonances that were either encountered or avoided in the past. We discuss prospects for observational tests of the growing frozen core model and possible implications for understanding the gas giants

Thermal and Tidal Evolution of Uranus with a Growing Frozen Core

The origin of the very low luminosity of Uranus is unknown, as is the source of the internal tidal dissipation required by the orbits of the Uranian moons. Models of the interior of Uranus often assume that it is inviscid throughout, but recent experiments show that this assumption may not be justified; most of the interior of Uranus lies below the freezing temperature of H2O. We find that the stable solid phase of H2O, which is superionic, has a large viscosity controlled by the crystalline oxygen sublattice. We examine the consequences of finite viscosity by combining ab initio determinations of the thermal conductivity and other material properties of superionic H2O with a thermal evolution model that accounts for heat trapped in the growing frozen core. The high viscosity provides a means of trapping heat in the deep interior while also providing a source of tidal dissipation. The frozen core grows with time because its outer boundary is governed by the freezing transition rather than compositional layering. We find that the presence of a growing frozen core explains the anomalously low heat flow of Uranus. Our thermal evolution model also predicts time-varying tidal dissipation that matches the requirements of the orbits of Miranda, Ariel, and Umbriel. We make predictions that are testable by future space missions, including the tidal Love number of Uranus and the current recessional rates of its moons

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