HR: 0800h
AN: DI41A-0344 [Abstracts]
TI: Self-Consistent Thermodynamic Description of Silicate Liquids
AU: * De Koker, N P
EM: dekoker@umich.edu
AF: Department of Geological Sciences, University of Michigan, 2534 C. C. Little Building, 1100
North University Ave, Ann Arbor, MI 48109, United States
AU: Stixrude, L
EM: stixrude@umich.edu
AF: Department of Geological Sciences, University of Michigan, 2534 C. C. Little Building, 1100
North University Ave, Ann Arbor, MI 48109, United States
AU: Stixrude, L
EM: stixrude@umich.edu
AF: Department of Earth Sciences, University College London, Gower Street, London, WC1E
6BT, United Kingdom
AB:
Describing the thermodynamic properties of dense liquids at extreme pressure and temperature is crucial to our
understanding of planetary processes including deep melting, magma ocean dynamics and lunar formation. The
functional form chosen to represent the equation of state should ideally depend on only a few parameters and
correctly account for kinetic and electronic contributions to the free energy at extreme conditions. High pressure
equation of state data for terrestrial liquids have mostly been fit to functional forms used for solids, such as the
high temperature form of the Mie-Grüneisen equation, which assumes a constant thermal pressure coefficient
(α KT). This approach is flawed since Maxwell relations require (∂ α KT / ∂ T)V =
(∂ CV / ∂ V)T and we have found in first principles molecular dynamics studies of
magnesiosilicate liquids at high pressure that the isochoric heat capacity (CV) varies significantly with
volume. Moreover, the Mie-Grüneisen equation of state does not yield the correct (ideal gas) behavior in the
limit of infinite temperature. Finally we have found that electronic contributions to thermodynamic properties are
non-negligible. With these constraints in mind, we develop a number of approaches to expressing the Helmholtz
potential over a large range of volume and temperature, including potential, kinetic and electronic contributions to
the free energy. From these expressions for the fundamental relation, internally consistent equilibrium
thermodynamic properties are derived by derivatives and Legendre transformations, which may be applied to the
exploration of a large array of problems in planetary science.
DE: 3611 Thermodynamics (0766, 1011, 8411)
DE: 3919 Equations of state
DE: 3924 High-pressure behavior
DE: 5460 Physical properties of materials
DE: 8124 Earth's interior: composition and state (1212, 7207, 7208, 8105)
SC: Study of the Earth's Deep Interior [DI]
MN: 2007 Fall Meeting