Combining computational and experimental approaches to the thermal equation of state of silicate liquids

Abstract:

Silicate liquids govern the dynamics and evolution of terrestrial planets, especially their early histories. Yet they remain among the least understood materials at deep interior conditions. Their importance arises from their mobility and concentration of key elements. Ironically, the difficulty of studying liquids arises from the related challenges of lack of fixed structure and multicomponent chemical complexity. Melts at extreme temperatures and pressures are also experimentally difficult to study, leading to sparse data coverage. A convergence of experimental methods and computational molecular dynamics (MD) models has moved us towards a general model of silicate liquids suitable for magma ocean, planetary impact, and core-mantle boundary situations. Among all the mechanical, thermodynamic, and transport properties, the thermal equation of state (EOS) — volume (V) as a function of pressure (P) and temperature (T) or internal energy (E) — is essential for both dynamic and thermodynamic models.

There are several variations on shock compression experiments, each optimized for precisely measuring specific aspects of the EOS: (1) super-liquidus, sealed-capsule shock travel time experiments give P-V-E along Hugoniot; (2) room T shock travel time experiments undergo shock melting and give P-V-E on an offset Hugoniot, giving as estimate of the Grüneisen parameter (γ); (3) warm glass, open-capsule, thick-flyer experiments yield P-V-E-T; and (4) warm glass, open-capsule, thin-flyer shots give T and sound speed. All four combined yield tight constraints on the near-Hugoniot thermal EOS, including precise values of γ at certain values of V and E. Applying this knowledge in a general framework to geophysically relevant P-T paths still requires judicious choice of the EOS formalism.

Finding the best formalism is best approached through MD simulations. The ability to arbitrarily and densely cover large swaths of phase space allows numerical models to suggest successful functional forms, trading their possible disadvantage of inaccuracy (especially with empirical MD) against wide-ranging internal consistency. Several groups have taken this approach. Our new model with an empirical γ(V, E) function favors simplicity, and can be fit to sparse shock data with notably better results than Mie-Grüneisen models.