Subproject 1: Thermodynamic properties of silicate solids and liquids and iron to the TPa range from ab-initio calculations

PI: G. Steinle-Neumann, PhD: F. Trybel

An improved description of the internal structure of exosolar super-Earths – which is one of the central goals of the Research Unit – requires a detailed knowledge of material properties at pressures and temperatures that significantly exceed those in the Earths interior, beyond 1 TPa and 10,000 K. Here we propose to investigate – by means of computational techniques – the structure and thermodynamic properties of three material types that are of central importance in planetary structure: (i) silicate and oxide solids, (ii) silicate melts, and (iii) liquid iron.

For the liquids, ab-initio molecular dynamics simulations will be performed with two goals:

  • Provide energies and pressures to fit a self-consistent thermodynamic model for liquids. The model is based on an expansion of Helmholtz energy in terms of temperature and finite Eulerian strain following previous work, and can be equally applied to silicate and metallic melts. The thermodynamic model for iron, in particular, will be useful in tightening constraints on the internal structure of cores in super-Earths (SP4).
  • To investigate possible phase separation in the silicate liquids. Here, the time-dependent mean-spare displacement and the evolution of the radial distribution functions from the molecular dynamics are analyzed to track the structure of melt components.
Thermodynamic model for liquid Al. Internal energy of the system, the P-V -T equation- of-state and the electronic contribution to entropy along isotherms are shown in three panel from left to right. Ab-initio MD results are shown by symbols, the global fit with the thermodynamic model of de Koker (2009) in the dashed lines. This figure is from Vlček (2012).
Radial distribution function of a Fe-bearing olivine liquid, with composition Fe12Mg24Si16O64 from MD simulations at 4,000 K and twofold compression (V/V0 =0.5, with V0 = 52.36 cm3/mol, the ambient pressure volume of forsterite at melting Lange (1987)). RDFs for the cation-oxygen pairs are shown in the left panel. Peaks in the Fe-O distances, both for the spin polarized (sp) and non-spin-polarized (nsp) simulations are virtually indistinguishable, but shifted to lower r relative to Mg-O. In the right panel cation-cation distances are shown for Mg-Mg, Fe-Fe and Fe-Mg pairs, both from the sp and nsp MD. Fe-Fe distances are significantly shorter than Mg-Mg distances, with magnetism slightly repelling the Fe pairs.

 

High pressure mineral phases beyond post-perovskite have been previously identified in ab-initio computations, and here we plan to follow up on investigating the stability and thermodynamic properties of these phases, using the self-consistent ab-initio lattice dynamics technique. As this method accounts for phonon-phonon interactions, it can stabilize phases that only occur at high temperatures and provides access to Helmholtz energy. Fitting the results to a Birch-Murnaghan Mie-Debye-Gr¨uneisen thermodynamic model for solids – again thermodynamically self-consistent – will provide an avenue to look in detail at phase stability, transition pressures and Clapeyron slopes. These results will be useful in the Research Unit for guiding and interpreting experiments (SP7 and SP8) and model results can be directly used in planetary structure models (SP4).

Contact PI

Ph.D. Gerd Steinle-Neumann
Bayerisches Geoinstitut, Universität Bayreuth, 95440 Bayreuth
T: +49 (0)921 55 3702 , Email