- Phasendiagramm (1) (remove)
- First principles phase diagram calculations in group IV carbides and Mg2SiO4 liquid from Molecular Dynamics (2009)
- Atomistic simulations on stability and physical properties of Earth materials are playing an increasingly important role in high pressure mineralogy. Such computations can provide guidance for experimental studies and insight into underlying causes of observations, or explore conditions and properties that are inaccessible to experiments at the current time. A variety of approaches have been applied in such research, with density functional theory based methods having become a reliable tool in computational mineral sciences. Despite this progress there are interesting problems which density functional theory based methods are not able to tackle on a routine basis. These include computations of phase diagrams and transport properties in liquids. The sub-solidus phase diagrams of the binary systems TiC-ZrC, TiC-HfC, ZrC-HfC at ambient pressure are computed based on electronic structure and energy calculations within density functional theory. Formation energies for a large number of supercells with compositions of (M1,M2)C, M1, M2 = Ti, Zr, or Hf, are computed by a plane-wave pseudopotential method. The energies serve as a basis for fitting cluster expansion Hamiltonians that are used to explore the sub-solidus phase diagram, i.e. stability of ordered intermediate compounds and the degree of miscibility in the systems by Monte Carlo simulations. Hamiltonians can be fit to the formation energies of the cells directly or after taking into account vibrational free energy. As it is prohibitive to compute vibrational free energy for all configurations they are approximated by the transferable force constant scheme: nearest neighbor force constants are computed for the end-member crystals with imposed but varying lattice parameters. The resulting bond stiffness versus bond length relationships are applied to the superstructures, using the relaxed bond lengths and their chemical identities as predictor. Significant miscibility gaps were predicted for the binaries TiC-ZrC and HfC-TiC, with consolute temperature in excess of 2000 K, in good agreement with experiments. The system HfC-ZrC shows complete miscibility at room temperature. Approximately symmetric phase diagram for HfC-TiC and asymmetric phase diagrams for HfC-ZrC and TiC-ZrC were predicted. With the success of the method in the simple carbide systems similar computations can now be performed for geologically relevant mineral families. Mg2SiO4 liquid at high pressure is of central importance in our understanding of melts that occur in the deep Earth and in particular in the early history of our planet, when it was in a magma ocean stage. Due to high melting temperatures little is known experimentally about its high pressure thermodynamic and transport properties that govern magma ocean structure and dynamics. Molecular dynamics simulations now fill this gap. Currently, density functional theory based computations are restricted to a few hundred atoms and a few picoseconds. While such simulations allow for determination of thermodynamic properties, longer run durations and larger cells are necessary to obtain transport properties such as diffusivity and viscosity with sufficient precision. By contrast, semi-empirical pair potentials provide an efficient route to perform large-scale molecular dynamics simulations. They suffer, however, from the fact that the transferability of the potentials to different conditions is not guaranteed. The development of aspherical flexible potentials that are fit to density functional theory results bridge the gap between ab-initio methods and classical potentials. Comprehensive large-scale molecular dynamics simulations using the aspherical ionic model were performed on Mg2SiO4 melt to obtain thermodynamic properties as well as diffusivity and viscosity. The pressure-temperature range covered was 0-32 GPa and 2600-3200 K. The thermodynamic parameters agree well with density functional theory based results: the Grüneisen parameter $gamma$ was found to increase significantly with pressure. Diffusivity is predicted to decrease and viscosity to increase with pressure. Both transport properties were readily fit with closed Arrhenius expression. Independent estimates on diffusivity and viscosity allows an examination of their relation through the Eyring equation, often employed to compute viscosity from diffusivity data. The proportionality factor between them, the translation distance for a diffusion event $lambda$, is determined as $lambda$=18 AA at 0 GPa, and decreases with pressure. This is in good agreement with previous molecular dynamics simulations using classical potentials, but significantly larger than other estimates of $lambda$ based on experimental data that yield 2.8 AA $ < lambda < $ 5 AA. Combining the thermodynamic and viscosity fits a magma ocean adiabat and the associated viscosity profile were computed.