Sound Speed and Temperature in Shock-compressed Silicate Liquids: Direct Constraints on Grüneisen Parameters and Heat Capacities
Abstract
Understanding the complete thermal equation of state (EoS) of silicate melts at pressures above 100 GPa is essential for describing the evolution of early terrestrial magma oceans and for interpreting the state of the modern core mantle boundary. The EoS must be accurate enough to assess the the density difference between melts and their coexisting solids and to extrapolate free energies as a function of composition, temperature, and pressure well enough to model phase equilibria. This requires both the definition and verification of a sufficiently robust functional form and the acquisition of precise data for calibration. The latest computational, thermodynamic, and experimental efforts to define buoyancy at the magma ocean liquidus do not agree; further refinement is needed.
We have recently added to our database of direct shock wave measurements of pressure (P) - Volume (V) - Energy (E) points from pre-heated silicate liquids by measuring shock temperature, in order to obtain constraints on the integral of the heat capacity at high P. Here we discuss a key modification of these experiments that uses a thin flyer plate to send a rarefaction wave catching up with the shock front. Measuring the overtaking time provides the velocity of the leading edge of the rarefaction wave, i.e. the bulk sound velocity in the liquid in the shock state. This measurement, together with the slope of the Hugoniot in P-V space, provides a direct, local measurement of the Grüneisen parameter. This is the first experimental test of the Mie-Grüneisen approximation for silicate liquids at high P. The first result is consistent with, but more precise than, the value fitted by comparing the cold solid and hot liquid Hugoniots of diopside-anorthite mix. Together two of these experiments also provide a local, rather than integrated, measure of the heat capacity. The improved knowledge of heat capacity and Grüneisen parameter allow the shock wave-based equation of state to be confidently applied to crystal/liquid buoyancy and phase equilibrium calculations at actual lower mantle liquidus and solidus temperatures. Long term, these data can be used to assess whether a formulation of the Helmholtz free energy (in V, T space) is in fact the best way to fit the EoS of a silicate liquid or whether an enthalpy formulation (in pressure-entropy space) works better.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2018
- Bibcode:
- 2018AGUFMMR31A..06A
- Keywords:
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- 3909 Elasticity and anelasticity;
- MINERAL PHYSICSDE: 3919 Equations of state;
- MINERAL PHYSICSDE: 7299 General or miscellaneous;
- SEISMOLOGYDE: 8124 Earth's interior: composition and state;
- TECTONOPHYSICS